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Mode coupling coefficients and impulse responses in a multimode graded-index fiber are investigated both experimentally and theoretically. Mode coupling coefficient measurements at 1.27 μm are made for a fiber before and after nylon coating. The fiber is 10 km in length and has no splicing point. The mode coupling coefficient change due to nylon coating is found to be relatively small. In the nylon-coated fiber, the coefficient increases monotonically as increasing a principal mode number, and the tendency is in good agreement with the theoretical prediction considering random bends along the fiber axis. With the increase in mode coupling coefficient and 0.01 dB/km of excess loss by nylon coating, 2.7 percent of increase in 3-dB bandwidth is observed. This increase in 3-dB bandwidth is explained by the theoretical calculation. The length dependence of 3-dB bandwidth exhibits a small mode mixing effect in the fiber. By the theoretical predictions based on the experimental mode coupling coefficients, the coupling length is estimated to be 25 km. It is also clarified that the length dependence of 3-dB bandwidth shows the L-0.5characteristic for km.